Consistency and Consensus Management in Decentralized and Distributed Systems

ABSTRACT

A method for achieving consensus amongst a distributed and decentralized set of computers, devices or components in a network interacting via messaging is presented. The method does not rely on the availability of an overall ledger that is consulted for every interaction. Rather, the interacting components communicate directly with each other via messages that contain proofs of consistency that may be used to achieve local consistency amongst the interacting components. Local consistency guarantees global consistency. For regulatory and record keeping purposes, use of an overall ledger may be contemplated for regulatory and record keeping purposes. The latter may be updated by the interacting devices via an asynchronous updating mechanism.

BACKGROUND TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application Ser. No. 62/651,410, filed Apr. 2, 2018, entitled “Consistency Management in Decentralized and Distributed Systems with Asynchronous State Maintenance”, the contents of which are incorporated herein by reference.

BACKGROUND

Distributed and decentralized systems are used in many computing applications where scalability and reliability are important requirements. Applications in transaction processing, digital rights management, cryptocurrencies, travel arrangements, access to resources, financial transactions, etc., make heavy use of distributed and decentralized systems of interconnected computers and components. In such applications, achieving consensus and maintaining a consistent view of the overall system is of great importance and has been the subject of many previous technological innovations and improvements.

Recent applications in cryptographic transactions (e.g., Bitcoin) use consensus methods that use enormous amounts of electrical power and the resulting transaction throughput rates are quite low. The present invention addresses these and other technological problems.

SUMMARY

In accordance with one aspect of the subject matter disclosed herein, a method is presented for transferring a state value from a first communication device directly to a second communication device. The method includes: requesting a data element from the second communication device; calculating a value of an irreversible function using the data element as an input to the irreversible function; encapsulating the state value in a data object using the calculated value of the irreversible function; transferring the data object from the first communication device to the second communication device; and wherein the first communication device can repeat the transferring of the state value only by solving the irreversible function in a reverse direction.

In accordance with another aspect of the subject matter presented herein, a method is provided of performing a transaction between a first communication device and a second communication device over a communication network. The method includes: requesting, with the first communication device, at least a first integer value from the second communications device, the first integer value being generated for use only in the transaction between the first and second communication devices, said first and second communication devices being provisioned with (i) first and second complementary cryptographic keys that are provided by a trusted party, the first key being usable to generate a proof that verifies that computer logic used a given input to produce a given output and the second key being usable to verify that the proof is accurate; (ii) a proof generating engine (PGE) that uses the computer logic and the first key as inputs and provides as outputs a first proof and a token that is an output arising from execution of the CP; and (ii) a proof verification engine (PVE) that uses the proof, the second key and the token as inputs and output indicating if the proof is accurate; calculating, with the first communication device, a first value of an irreversible function that uses as an input the first integer value received from the second communication device; executing in an atomic operation, with the first communication device, the computer logic to generate the token and a first proof and permanently delete the first integer value, the first proof being usable to verify that the computer logic generated the token, the token including (i) a state value that is to be transferred from the first communication device to the second communication device, (ii) a second value of the irreversible function, the second value of the irreversible function being calculated by a third communication device that transferred the state value to the first communication device, wherein the input to the irreversible function when calculating the second value includes a second integer value received by the third communication device from the first communication device and (iii) a product of the first value of the irreversible function and the second value of the irreversible function; and sending, in one or more data messages, the token and the first proof to the second communication device from the first communication device.

BRIEF DESCRIPTIONS OF THE DRAWINGS

FIG. 1 shows an example of a Bitcoin-style decentralized transaction processing.

FIG. 2 shows the mode of interaction between two client devices in a Bitcoin-style network.

FIG. 3 describes the problem of decentralized transaction processing without a blockchain/ledger.

FIG. 4 shows an arrangement by which decentralized transaction processing may be achieved with asynchronous updating of the blockchain or a distributed database acting as a record-keeper and not being in the path of the transaction.

FIG. 5 shows an alternative arrangement corresponding to FIG. 4.

FIGS. 6A and 6B show models for an exemplary transaction.

FIG. 7A shows an exemplary commitment function and token.

FIG. 7B shows an exemplary verification of tokens.

FIG. 8A shows a review of program proof technology.

FIG. 8B shows exemplary encapsulated messaging/transaction traffic.

FIG. 9 shows an exemplary succinct notation for transactions.

FIG. 10A shows a device with a trusted execution environment.

FIG. 10B shows an arrangement for running a selected program using the engine PGE.

FIG. 10C shows a method for running one of the programs, Transfer, Split/Transfer or Merge using the engine PGE.

FIG. 10D shows a method for running the program GCT using the engine PGE.

FIG. 11 shows a method by which transactions are supported in a decentralized network with asynchronous updating of the record-keeper.

FIGS. 12 & 13 show the method “Transfer” and its corresponding flow chart.

FIG. 14 shows the method of program Generate Commitment Trigger (GCT).

FIG. 15 shows a succinct notation for an exemplary transaction.

FIGS. 16 and 17 show execution plans for a “Split/Transfer” transaction between client devices.

FIGS. 18 and 19 show the method “Split/Transfer” and its flowchart.

FIG. 20 shows the succinct transfer representing the “Merge” transaction.

FIG. 21 shows the execution plan for the “Merge” program.

FIGS. 22 and 23 shows the method and flow chart for the “Merge” program.

DETAILED DESCRIPTION Motivation

Transaction processing systems comprise databases, application programs, state monitoring systems, and networks of multiple devices. They occupy a basic place and play a fundamental role by providing support to data operations in communications, finance, manufacturing, travel, entertainment, crypto-currencies and process control.

A database is a dataset that represents the state of a physical or an abstract system. A request or a query is a computer program/command that returns the (current) state of the database. A transaction is a collection of one or more computer programs that transform the state of the database system into one or more new states. A transaction processing system is a collection of computer programs running on computing devices providing operational support for transactions. A distributed system is a collection of inter-connected computers communicating using one or more communication (messaging) protocols. A decentralized system is a (distributed) system in which no single entity controls all the computers.

Maintaining consistency or achieving consensus under state changes is a crucial requirement for transaction processing systems in distributed and decentralized systems and finds its expression in many applications.

In fault tolerance applications the consensus problem relates to ascertaining the reliability of inter-connected computers/components. A group of inter-connected computers may communicate with each other via messages. One or more of the connected computers may become faulty and send out conflicting messages, e.g., it may send messages indicating it is faulty to some components and that it is functioning properly to other components. The problem is to detect faulty components from the received messages and reach consensus throughout the network.

In crypto-currencies and financial transaction systems the consensus problem is usually described as the “double-spend” problem wherein a user (or a group of users) maliciously conspire to spend more than their amount balance. In Bitcoin-style networks (cf. FIG. 1) users may transfer their “unspent transaction outputs” (UTXO) to other users. The problem is to reach consensus amongst the computers managing or executing the transactions that no double-spend events have occurred.

Consider a user, say Alice, having a certain amount of UTXO. In order to transfer some of her spending rights to another user, say Bob, she initiates a transaction request assigning her spending right to Bob by using Bob's address (a hashed number represented by a bit string) and “signs” the transaction by using Bob's public key. (It is well-known that a signed transaction can only be accessed by a user possessing the corresponding private key.) In turn, Bob wishing to transfer the spending right transferred to him by Alice to another user, say Charlie, accesses the transaction using his private key. The UTXO and the associated transfer of spending rights are called transactions that are recorded in a ledger called the blockchain. On occasion, the terms “blockchain” and “ledger” may be used as synonyms.

Generally, the ledger preserves the integrity of the system's transactions and is the sole arbiter of the history of the transaction system. Any third-party client may verify the integrity of a public ledger by re-building the ledger from its initial state. Thus, the blockchain represents the correct and true history of the network. All Bitcoin clients (also called wallets) are user interfaces displaying the state of the data on the blockchain. For example, a wallet displaying a balance of a user shows the UTXO of that user as reflected by the data on the blockchain.

One or more users may conspire to double-spend their UTXO and thus corrupt the blockchain. To avoid the double-spend problem and maintain consistency of or consensus on the blockchain, Bitcoin-style networks use a method that may be described as follows.

A group of inter-connected (networked) nodes, called miners, are especially configured to perform a certain computing task or “work” and provide “proof” that the task or work has been completed. The idea is to determine the first node that provides a successful proof (of work). Each miner receives transaction requests from clients (wallets) and records the requests in a local memory called the “block”. All requests received by a miner are broadcast to all the other miners. Thus, every miner has its own identical block of received requests.

We are now required to select one of the miners and allow him to add his block of transactions to the blockchain. The selection metric is the proof of work. A miner announces that it has successfully performed the work and provides a proof. The proof is verified by one or more of his contemporaries, i.e., other miners. Upon verification, the successful miner may add his block to the blockchain. (The verification involves checking the integrity of transactions in the block against the transactions in the overall ledger.)

Inconsistent transaction requests received by two miners cannot be added to the blockchain since only one miner is selected and his block is checked and verified before it can be added to the blockchain. Thus, the proof of work metric may be said to prevent the double-spend problem. Alternatively, we may state that the method to achieve consensus is based on the proof of work metric. An additional step may be added to the above procedure for taking care of network-splits. In relevant literature, the above method by which new blocks are added to the overall blockchain is sometimes referred to as the “eventual consistency” algorithm.

As defined, the proof of work metric requires increasing amounts of computational effort and thus inherently consumes increasing amounts of time and computing resources, e.g., consuming electrical power and requiring special-purpose hardware. Thus, the transaction processing rate of the network, i.e., the number of transactions per unit of time, has to bear the computing load. It is well-known that Bitcoin-style networks do not provide sufficiently fast transaction rates for some types of transactions. Some calculations available in the literature suggest a transaction rate of approximately 7 transactions per second, while other calculations suggest that the Bitcoin mining network uses more than twice the amount of electricity as that used by Scotland, i.e., about 52 terrawatt hours. In contrast, the Visa network processes 65,000 transactions per second (at maximum capacity) using ½ of 1% of Bitcoin's usage. Some variants of Bitcoin such as Lightning claim much faster throughput rates by defining new kinds of transactions, e.g., by supporting off-chain transactions by setting up payment channels between pre-determined parties. New consensus algorithms such as “proof of stake”, “proof of authority”, etc. have been proposed to reduce the workload required to maintain the blockchain. All such consensus seeking methods use the blockchain mechanism but differ in the manner of selecting a miner node.

Thus, maintaining the consistency of the blockchain costs dearly and slows down the transaction rate to unacceptable levels for many applications.

In one aspect, the present invention is concerned with avoiding the use of blockchain to maintain consistency by providing mechanisms that allow two client devices (e.g. two applications such as wallets residing on the client devices) to transact directly with each other without being able to initiate double-spend transactions.

Since our method avoids the use of blockchain mechanism to guarantee transaction integrity or consistency, relegating the use of blockchain to an optional and asynchronously maintained record-keeper or log in certain embodiments, we save enormous amounts of electrical power. Concomitantly, two transacting devices may operate at the speed of the underlying communication network, thus improving the transaction throughput.

It is important to note that in Bitcoin-style networks, no two client devices (wallets) interact directly. All wallet interactions are indirect in the sense that interactions take place through the blockchain. That is, device to device interactions are achieved by a first client device signing a transaction (Tx) on a block of the blockchain and a second device accessing the same transaction in a subsequent block of the blockchain (cf. FIG. 2) and responding with a new transaction. As explained earlier, the two devices may sign the transactions using each other's public keys. Thus, the blockchain is the medium of interaction.

In contrast, we consider a network of inter-connected client devices (cf. FIG. 3) wherein the client devices 301 and 302 communicate directly with each other via a messaging medium. For regulatory and other reasons such as audit trails, the network may utilize a record keeper (303), but it is not mandatory in the present invention and does not lie in the “path” of the transactions. (In related work we show the utility of a ledger, e.g., in reconstructing a user's wallet who loses his client device.) It therefore does not contribute to transaction overhead. The record keeper may be updated by both the client devices at any time after the transaction between them has committed. The two client devices need not synchronize their updates of the record-keeper with each other or with the transaction process. We refer to such an updating policy as an asynchronous update of the state of the record-keeper.

As used herein, client devices (or simply “devices”) refer to communication devices such as mobile phones, personal digital assistants (PDAs), smartphones, desktop computers, wearable smart devices (e.g., fitness bands, smart bandages), tablet computers, GPS devices, gaming consoles, laptop computers and transponders, which are able to communicate over one or more wired and/or wireless communication links that may or may not involve a communications network such as the Internet, Wi-Fi and Bluetooth.

As shown in FIG. 3, a central problem to be solved is for device D2 (302) to trust the transaction from device D1 (301) and ensure that D1 cannot double-spend. In subsequent discussions we show the system and methods of the present invention and use the above case as an exemplary problem.

In embodiments, the record-keeper may be implemented as a blockchain system using a miner selection metric based on proof of work or proof of stake, etc. Network designers may prefer such embodiments since the blockchain mechanism, after a decade of use, is trusted to withstand hacking and corruption attacks. As used herein, since the blockchain is not in the path of the transaction, it will not negatively impact the transaction rate of the system and cause undue workload/stress on the network's resources. It should be noted that the present invention inherently avoids the need for a blockchain system, which in all cases is discussed herein as an optional feature that may be used for recording-keeping if desired.

FIG. 4 shows one such arrangement. An especially designated node called “M” performs, inter alia, two functions described as follows.

-   -   1. Provision client devices with account balances, e.g., D1         (401) and D2 (402) so that D1 and D2 have balances B1 and B2,         respectively.     -   2. Client devices, e.g., Devices D1 and D2, report transactional         data to “M” (403) after the transaction has occurred         (committed). “M” (403) may, in turn, update the blockchain (or         distributed database system in some embodiments) asynchronously         acting as a record-keeper (404).

In embodiments, “M” may be implemented, for instance, as software running on one or more computers, e.g., a server complex, a server farm, etc.

FIG. 5 shows an alternative arrangement wherein “M” comprises a device (501) running a computer program operating on a blockchain. The computer program may be configured to asynchronously communicate data received from devices D1 (503) and D2 (504) to the blockchain (502). It may also be configured to operate according to business logic as per the requirements of the networking application being implemented by the network. Such computer programs are often called smart contracts.

In this regard, it is pertinent to discuss certain prevalent systems that allow “off-chain” operations, in which operations involving the ledger may be deferred for a time. Such deferments usually involve “trusting” a non-mining entity to “verify” a transaction without an ironclad guarantee based on the system ledger itself. An intermediary node may issue a commit for a series of deferred transactions. However, the ultimate commitment of the system in such a case is not guaranteed and a user may not assume that the transactions have committed in actuality.

In one variation of deferred commitment schemes, the so-called payment channel method, two parties (client devices) wishing to engage in a deferred transaction, set up a payment channel in advance of the transaction. The blockchain records the “intended” transaction. At a later time, the two parties may transact the previously set up transaction. In certain embodiments, intermediate devices may facilitate the transaction by acting as proxies. Thus, nodes “A” and “C” may set up an a priori payment channel. Next, “A” may interact with node “B” and node “B”, acting as an intermediary, may transact with “C”.

Certain Technical Contributions of the Present Invention

The systems and methods described herein pertain to certain improvements to the technology of transaction processing systems in communication networks. Certain aspects of such improvements may be described, without limitation, as follows.

We propose technologies that support transactions between client devices in which each client device may contain a complete verifiable record of its transactions, without needing to maintain a record in a ledger-based blockchain system or other such state maintenance systems. A set of asynchronous operations may be used to update a state maintenance system, but the invention does not rely on the existence of such a system, nor does it need it in any basic manner.

Each client device may engage in one or more transactions and maintain a record of its own transactions. (A client device need not designate an intended recipient, i.e., no payment channel needs to be set up, etc.) The record so maintained may be used in conjunction with methods described herein to verify the consistency of the transaction. That is, transactional consistency may be checked locally, i.e., consistency checking may involve only the two client devices involved in the transaction. However, local consistency implies global consistency in the invention presented herein. That is, every transaction between two client devices that commits is guaranteed to be both locally and globally consistent. Consistency maintenance includes ensuring the satisfaction of the double-spending constraint.

In one aspect, certain advantages of the present invention arise from a specific type of data structure, referred to herein as a “token,” which is designed to improve the way systems store, track and process data.

The present invention reduces the latency of crypto-currency networks in particular and consensus creating methods in distributed networks in general. The concomitant increase in transaction output rate will be significant and will considerably improve the usability and practicality of the technology, thus increasing its general acceptance by the public. The cost of the infrastructure supporting the distributed networks will be considerably reduced since no mining and very little hashing operations will be needed. Finally, the reduced workload of the methods presented herein will contribute to reducing the use of electrical power by the network infrastructure and thus contribute to the improvement in the carbon footprint of the overall system.

The methods of the present invention may apply not only to financial applications such as crypto-currencies, but to a variety of applications including, without limitation, messaging, email, digital content sharing, music sharing, entertainment, travel, digital wallets and credit cards, etc.

In one aspect, the systems and techniques pertain, more generally, to a communications network wherein rights and capabilities are transacted between client devices that serve as network nodes. The rights and capabilities so transacted may be maintained and verified by examining only the state of the devices involved in the transactions. There is no mandatory requirement to consult or maintain a global state maintenance system.

Furthermore, the technology presented herein is applicable to devices engaging in machine-to-machine transactions, possibly involving micro-transactional amounts, for example, autonomous cars making toll payments to roadway toll collection devices.

Basics of the Transaction Model

Client devices are used to represent users of the network, which in some embodiments are pre-provisioned with computer programs or other executable computer code that enable the client devices to transact with each other. We assume an underlying communications network that allows client devices to interact with each other, i.e. send and receive data from other client devices. Thus, each client device is assumed to have a network address, i.e., a bit string, that may be used to locate the client device.

In certain embodiments, communication protocols (e.g., I2P, TOR, etc.) may be used by a network that obfuscates the addresses of client devices. We do not discuss this aspect of the communication protocol herein and consider our invention to be independent of such technologies. That is, we assume an underlying mechanism by which two client devices may communicate with each other using addressing mechanisms that may or may not be obfuscated.

Briefly (cf. FIG. 6A), our transaction model involves two client devices in which a first client device, usually referred to as the initiating device, may initiate a transaction with a second recipient device. The initiating device requests a data item (called the commitment trigger) from the recipient device and runs a computer program to create two data structures called the token, say “T” and a first proof data object, say P1. The token “T” represents the transference of “spending rights” from the initiating device to the “receiving” device. The first proof object, P1, is meant to “verify” the successful running of the computer program effectuating the creation and transference of the token. (In subsequent discussions, we describe the terms “proof”, “token” and “verify” in more detail.)

Concomitantly, the recipient device, upon receiving the request for a commitment trigger, runs a computer program to satisfy the received request and generates a second proof data object, P2, meant to verify that it generated the requested commitment trigger.

In crypto-currency applications, the token data structure represents a “spending right” that is transferred from one client device to another. As such, the token data structure will contain (in one of its data fields) the balance/amount that can be spent. Additional fields of the token data structure will contain data computed as described later.

We now explain our basic transaction model with recourse to FIG. 6B.

Notation:

We denote commitment triggers by the symbol r_(xy) in which the subscripts “x” and “y” denote that the commitment trigger was generated by client device “x” and sent to client device “y”. Also, client devices referred to by numeric names, such as client device “1” or client device “2”, etc., typically denote client devices involved in past transactions. When considering client devices involved in a current transaction, we use alphabetic names for client devices, e.g. client device “A”, client device “B”, etc.

Let us assume that client device “A” has concluded a (previous) transaction with client device “1”. During the course of this transaction, client device “1” asked and received a commitment trigger, r_(A1), from client device “A” and used it to create and send a token to client device “A”. (That is, client device “A” sent a commitment trigger on request to client device “1”; the latter used the received commitment trigger to create and send a token to client device “A”.)

Thus, client device “1” transferred its spending right to client device “A”, represented by the token received by “A”. (As will be shown later, client device “1” will lose its capability to double-spend its spending right.) Client device “A” saves the commitment trigger, r_(A1), it provided to client device “1”.

Thus, at the conclusion of the transaction with client device “1”, client device “A” has a token received from client device “1”. This token now represents the spending right acquired by client device “A”. Client device “A” also has the commitment trigger r_(A1) it had provided to client device “1” during the previous transaction. The token received from client device “1” has a balance representing the acquired spending right.

Let us now assume that client device “A” wishes to transfer its (acquired) spending right to client device “B”. It may do so by creating a new token with a new balance (that is less than or equal to the spending right it acquired). To create the needed token, client device “A” requests and receives a commitment trigger, r_(BA), from client device “B”. Client device “A” may now construct the new token using its two commitment triggers, r_(A1) and r_(BA) with the new balance and transfer it to client device “B”, representing that client device “A” has transferred a spending right to client device “B”.

We thus see that, generally, our transaction model involves the transference of tokens from one client device to another, the tokens representing spending rights. To execute a transfer of spending right, a client device needs an input token and two commitment triggers in its memory that it may obtain either as a result of previous transactions or via a provisioning step, e.g., when the client device is being set up.

Having transferred a spending right, we require that the same right cannot be transferred again. As will be shown in more detail later, client device “A”, when transferring the newly created token to client device “B”, is required to delete the commitment trigger that it had saved during the previous transaction with client device “1”. Thus, it is effectively unable to re-compute the needed output token.

Commitment Functions and Tokens

We now describe the notion of tokens further by discussing the computation that yields values that populate the token data structure. We use the words “calculate” and “compute” interchangeably in the descriptions that follow.

The token data structure depends on a type of calculation or function called a commitment. The basic idea behind the calculation is that it is easy and efficient to calculate in one “direction”, but no known efficient method is known to calculate it in the “reverse” direction. Many different types of commitment functions may be defined using the notions of complexity in computer science theory. In literature, such functions are also referred to as irreversible or one-way functions.

Consider the following irreversible function F (also shown in 701 cf. FIG. 7A) that will be used in the descriptions that follow. We emphasize that the function “F” as defined herein is illustrative of a general class of functions known in the literature.

F(r,m)=(g ^(r) *h ^(m))mod p,

where g, h and p are primes and r and m are integers. Generally, we will be concerned with calculating the value of the function F with respect to a given value of “r”. We use the notation “C” to denote the value of the function F for a given value of “r”. Thus, F(r,m)=(g^(r)*h^(m))mod p=C.

Let

F(r ₁ ,m ₁)=(g ^(r1) *h ^(m1))mod p=C1,

and

F(r2,m2)(g ^(r2) *h ^(m2))mod p=C2

Then

C1*C2=((g ^(r1+r2) *h ^(m1+m2))mod p)=C12

Consider a client device with a known (integer) network address “m1”. It is then easy and efficient to calculate C1 if we are given “r1”. However, solving for “r1” requires solving the discrete log problem for which no efficient solutions are known (as is well-known in the literature). Thus, appropriate choices of g, h, m, r1, etc. give a probabilistic guarantee that C1 can only be computed in one direction, i.e., we can compute C1 given “r1”, but we are effectively unable to compute “r1” given C1. In embodiments used herein, r1 and r2, etc., may be randomly generated integers and will be referred to as commitment triggers. The variables m1, m2, etc. denote integer addresses or other identifiers of the transacting client devices. Of course, more generally, any suitable parameter values may be used for r and m. More generally still, the parameters that are used as inputs to the particular irreversible function that is employed may vary from system to system. For purposes of illustration, however, the discussion herein will employ the commitment function F with the input parameters r and m as defined above.

(On occasion, in commitment calculations, in addition to the parameters C1 and C2, we define a third parameter C3 (=F(r3,m3)=(g^(r3)*h^(m3))mod p) and then define C123 as the product C1*C2*C3.)

Exemplary token data structures are shown in FIG. 7A (702) and also in FIG. 17 as 1710 and 1720.

In the present invention, we use the computational hardness of the discrete log problem (or other such hard problems known in literature) to define the commitment function and to get a probabilistic guarantee that a computer program designed to compute the commitment function cannot be successfully executed.

As briefly described above, a transaction typically involves an initiating device and a recipient device. In such situations, the initiating device requests a commitment trigger from the receiving device.

We have used the parameter “m” in defining the commitment function F above as the address of the client device. In embodiments, commitment functions can be described without such a parameter, i.e., one may only use the commitment trigger as the parameter. Our usage of the address of the client device as a parameter herein stems from our aim to identify the client device performing the indicated calculation. To this purpose, we may alternatively use the serial number of client devices, CPU numbers, or other identifiers that may serve to identify the client device.

Additionally, we may also use the public key of the user as the value of the parameter “m” to identify the user of the client device. As is well-known, a public key can be verified by using a private key known only to the user of the client device. In such usage, the public key is encrypted using a hashing function. When verification is needed, the encrypted public key may be decrypted and verified against the user's private key.

It is well-known that certain one-way functions, such as the Integer Factorization or the Discrete Logarithm functions, are vulnerable to attacks using quantum computers. However, current literature proposes several functions that may be used in lieu of one-way functions known to be vulnerable. Examples of such functions, without limitation, are the NTRU Encrypt, Rainbow, SPHINCS, BLISS-II, New Hope, SIDH, etc. These and other such functions are postulated to be secure against attacks by quantum computers and the present invention envisions using them in calculations involving commitment functions. Details of such so-called “post quantum cryptographic functions” may be found in “Kop, Cetin Kaya (ed.), Open problems in mathematics and computational science, Springer 2014, ISBN 978-3-319-10683-0, 2014”. See also, “Bernstein, Daniel, et al., Post quantum cryptography, Springer 2013, ISBN 978-3540887010”.

We now turn to the question of constructing and verifying token data structures using the above exemplary transaction from initiating device “A” to recipient device “B” (FIG. 6B). As explained earlier, device “A” requests and receives a commitment trigger, r_(BA), from device “B”. Device “A” now computes C_(BA)=F(r_(BA), m_(A)) and C_(A1)=F(r_(A1), m_(A)) where m_(A) is the integer address of device “A” and r_(A1) is the commitment trigger it provided to device “1” from whom it acquired spending rights. Using C_(BA) and C_(A1), device “A” may now compute the product C_(A1)*C_(BA).

The corresponding token data structure comprises the values computed above and is denoted as token(Amount, C_(A1), C_(BA), C_(A1)*C_(BA)). However, the token sent to device “B” as a part of transferring spending rights does not contain C_(BA), i.e., the component value corresponding to the commitment trigger r_(BA). That component value of the token is left blank and is filled in, for verification purposes, by the recipient device using its commitment trigger.

Recall that the component value C_(BA) may be efficiently calculated using the commitment trigger r_(BA). Without the commitment trigger, we need to calculate the discrete logarithm, i.e., we need to solve for X in

(C _(A1) *C _(BA))/C _(A1) =F(X,m _(A))

FIG. 7B illustrates the above description with reference to the exemplary transaction shown in FIG. 6B.

Device “1” having received commitment trigger r_(A1) constructs token T_(1A) denoted as

Token_(1A)=(Amt1,C1,blank,product1)

where “Amt1” is the amount of spending right to be transferred, C1 is the component value computed by device “1” using a commitment trigger received from a previous transaction, the missing or blank value represents the value computed using the commitment trigger r_(A1) received from device “A”, and product1 represents the value obtained by multiplying the latter two component values.

To verify the token, device “B” performs the function 100 indicated in FIG. 7B.

Similarly, device “A” may now use its two commitment triggers to compute C_(A1)=F(r_(A1), m_(A)), C_(BA)=F(r_(BA), m_(A)) and C_(A1)*C_(BA). It may then construct the token token_(AB)=(Amt2, C_(A1), blank, C_(A1)*C_(BA)) where the “blank” value represents C_(BA). Device “B” may verify the received token by performing the calculation shown as 200 in FIG. 7B.

Finally, the token data structure contains a data field that, in currency applications, may be used to convey monetary amounts in a transaction. In non-currency applications, such a data field may be used to convey other types of information, e.g., in fault-tolerance applications, the data field may be used to convey the status of various components or devices in the network.

The Technology of Proof of Program Executions

In the discussion above, we briefly discussed the notions of commitment triggers and tokens and the general model of transactions. In this section, we describe the notion of “proofs” of program executions.

The technology of proof of program executions is concerned with verifying that a given program executed (“ran”) with a given input and produced a given output. The execution of a computer program on a given input resulting in a given output may be said to represent a statement, viz., “the program ran on the <given input> and produced <given output>”.

In one embodiment, program proof technology compiles input programs into pseudo-code and runs the latter in a suitably instrumented run-time environment. For example, programs written in a (subset) of the C programming language may be compiled into an assembler language and executed on an instrumented virtual (software) computer that supports the assembler instruction set. (Other such instruction sets and instrumentations may be defined and are known in the literature.) A given program when executed in such an instrumented environment produces its output and a trace of its execution due to the instrumentation. The trace represents the states of the computation, e.g., contents of registers and memories of the virtual computer, values of variables, etc., as a result of the execution of the given program. To verify that the execution actually occurred, we can verify the trace to ascertain that each state follows from the previous state, resulting in the given output. Since the trace could only have been produced by the execution of the program in the instrumented environment, we may then take the trace to be a “proof” of the execution of the given program. To ensure that the trace has not been altered in any way, it may be encrypted by using encryption key technology.

In summary, proof technology is a set of methods (encapsulated in computer programs, also called software engines) that verify executions of programs. That is, a computer program runs, and a trace/record of the program is produced in such a manner that the (alleged) execution may be verified by processing the trace. The trace may be referred to as the “proof”, i.e., the data object “proof” serves to verify the execution of the program. In a sense, every computer program when run on a given input and producing a certain output may be thought of as a statement, viz., the program ran on the given input and produced the indicated output. A proof of the execution of the program may then be taken to verify the statement representing the program's execution.

As a simple example, consider a program that multiples two integers to produce a resulting integer and let it accept as input the integers X and Y and produce as output the integer, Z. A proof of the execution of the program may then be taken as a verification of the statement “the program ran on input X and Y and produced output Z”.

For more details, see cf. Snarks for C: verifying program executions succinctly and in zero knowledge, by Eli Ben-Sasson, et al., https://eprint.iacr.org/2013/507.pdf. Also, patent application Ser. No. 15/671,021 extends program proof technology in various ways (e.g., in producing proofs of user data privacy and sharing of content between computer programs). In the present invention, we further extend program proof technology to solve the double-spend problem in decentralized and distributed systems.

As mentioned above, the technology of proof of program executions encapsulates given computer programs in software engines. In particular, we outline three such software engines as follows (cf. FIG. 8A).

-   -   Key Generating Engine, KGE (801)     -   Proof Generating Engine, PGE (802)     -   Proof Verification Engine, PVE (803).

The engine KGE (801) takes as input an exemplary program, CP, and produces two keys as output, P_(k) and V_(k). The purpose of the keys is mainly to ensure cryptographic security of data objects produced as described below.

The engine PGE (802) takes the following inputs:

-   -   The key P_(K) produced by the KGE above.     -   The computer program, CP, that was input to the KGE.     -   The input token(s) needed by the inputted computer program, CP.

PGE runs the program inputted to it with the given input token(s). The inputted program produces an output, say “output token(s)” and PGE produces a proof object, P, for the given input if it runs successfully. Otherwise, it produces an error response.

The engine PVE (803) takes as input the proof object, P, produced by PGE above, the key V_(k) produced by KGE above, and the output token(s) produced by the computer program, CP, inputted to PGE above. It produces a “yes” response if the proof P is linked to the indicated output token(s) via the keys V_(k) and P_(k) (since the latter two keys are complementary). Otherwise, it produces the response “no”.

In embodiments, the key(s) V_(k) may be provided to one or more client devices in the network. In alternative embodiments, the keys V_(k), may be provided to one or more distinguished nodes, called validator node(s) in the literature. Note that the running of the engine KGE is a one-time operation whereas PGE may be run whenever additional proofs are needed.

The general process of validation using the V_(K) keys is as follows. As mentioned earlier, client devices represent users of the network. As these devices engage in transactions, spending rights are transferred between client devices as tokens created by specifically designed computer programs. It is essential that the tokens be validated as being produced by the specified programs. Further, that the programs producing the tokens are uncorrupted from their original provisioned form. This is accomplished by the validator nodes using the V_(K) keys. That is, generally, a client device receiving a token representing spending rights, requests a validator node to validate the received token. The validator node uses the key V_(k) corresponding to the received token and the engine PVE as described above.

Encapsulating Messaging/Transaction Traffic

As mentioned earlier, we use user (client) devices to represent users of the network. As these devices engage in transactions, they send and receive data messages representing the transference of spending rights. The resulting data traffic is managed in a way that the history of the transactions may be re-constructed securely as and when needed.

FIG. 8B shows an exemplary scheme wherein device “1” sends a data message to device “A” that, in turn, sends a data message to device “B”, etc. The data message from device “1” to device “A” comprises of token_(A1) and a proof P_(A1). We create a hash of the concatenation of the latter two data objects, using a well-known hashing function such as SHA-3, etc., shown in cell number 3 of 100, FIG. 8B.

The data message from device “A” to device “B” is shown as 200, FIG. 8B. Note that message 200 contains a hash of the previous message 100.

Note also that the transaction data from device “A” to device “B” contains the proof, P_(1A), from the previous transaction. Generally, transaction data from an initiating device will contain proofs of all previous transactions (except as noted later), thus enabling recipient devices to re-construct the entire proof chain. As will be shown later, this enables a recipient device to verify all previous transactions.

As will also be described later, a device may (asynchronously) update the network's record-keeper with transaction data from the transactions that the device may have undertaken. A device that has executed such an update procedure is referred to as a “synced” device. The latter may, after a sync, delete its previous proof chain since the record-keeper will contain the necessary transaction data.

In order to simplify the following descriptions, we will assume that both the initiating and recipient devices in a transaction are synced devices.

Succinct Representations of Transactions

Having briefly described messaging or transaction traffic between devices, it is permissible to describe a succinct representation of the same as shown in FIG. 9.

In 901 (cf. FIG. 9), we show an exemplary transaction from device “A” to device “B”. We observe that both devices may operate independently and interact by sending data to each other. We describe the actions of each device independently below.

Device “A”:

Launches engine PGE with one of the programs Transfer, Split/Transfer or Merge (described later), being selected as input to the PGE. As will be seen from its specification, the selected program requests a commitment trigger, r_(BA), from device “B”. Next, the selected program produces a token, say T, output data “Bal” and terminates. The PGE produces a proof object, say P1. We can summarize the above actions as “device A uses the selected program and PGE to produce a proof P1, token T and data “Bal”. We may represent the interactions of device “A” succinctly using the representation shown below.

Device A[PGE/CP]{P1}{T}{Bal}

where “CP” denotes one of the programs “Transfer”, Split/Transfer”, or “Merge”.

Device “B”:

Launches engine PGE with program Generate Commitment Trigger (GCT), also described later, that responds to the request from device “A” by generating a commitment trigger. GCT outputs the requested trigger and PGE produces a proof, say P2. We may summarize the actions as “Device B uses the PGE and program “GCT” to generate a commitment trigger and produces a proof, P2. We may represent the actions of device “B” succinctly using the representation below (reading from right-to-left):

{P2}[PGE/GCT]Device B

Combining the two interactions into a single form, we get

<Device A[PGE/CP]{P1}{T}{Bal}:{P2}[PGE/GCT]Device B>

where the angular brackets “<” and “>” are used as delimiters and the colon symbol “:” separates the two individual interactions. We refer to the latter expression as the succinct representation of the interaction between the named devices, “A” and “B”. It is also shown as 902 in FIG. 9.

Generally, the succinct representation above, may be described as having the form “<Interactions of initiating device:Interactions of recipient device>”. The interactions of the initiating device will always involve one of the programs “Transfer”, “Merge” or “Split/Transfer” that produce a proof, token(s) and output data. The interactions of the recipient device always comprise the program “GCT” producing a proof. Note that the succinct representation does not show the commitment trigger since, as will be seen, it will be deleted by design.

We remark that the above succinct notation denoting transactions is meant only for pedagogical reasons and that the actual traffic may use the encapsulations described earlier.

Trusted Execution Environments and Trusted Devices

In an embodiment of the present invention, the client devices in the communication network contain trusted execution environments (TEE) housing the computer programs described below and the data that they operate upon. A user or operating system (OS) application running in a parallel processor may trigger the housed computer programs via an API provided by the system/device. A trusted device is one that contains a TEE.

TEE is an isolated environment composed of hardware and software that runs in parallel with the operating system. It provides a trusted execution environment for computer programs, safeguarding them from software and hardware attacks. The housed programs have access to a storage area within the TEE that they may use to store and read data objects. Software and cryptographic techniques protect the housed computer programs from each other and from (OS or user) applications running in parallel processors.

As is well-known, a hardware-based root of trust is used in a TEE. Thus, an attacker needs to extract root keys from the hardware. In some implementations, extraction of the root keys via reverse engineering or via hardware probes either destroys the keys or may slow down the probing processes. In some cases, an extracted key may only work on one chip/hardware and be useless for all other chips.

TEE based computer systems and devices have been proposed and discussed in industry associations such as Global Platform and Trusted Platform Module.

In the present invention, as shown in FIG. 10A, we assume that the TEE of client devices are pre-provisioned with computer programs, token(s) and commitment triggers. That is, the TEE's processor(s) run computer programs and the data store contains tokens and commitment triggers. FIG. 10 shows an exemplary trusted device whose TEE processor is pre-provisioned with exemplary computer programs, Transfer, Split/Transfer, Generate Commitment Trigger (GCT) and Merge. These programs are further described below. The storage area of the TEE contains tokens and commitment triggers that the illustrative programs operate upon.

Running Programs in Trusted Devices

In embodiments, the client devices in a communications network are provisioned with trusted execution environments (TEE). In a provisioning step, the TEE of client devices in the network are provisioned with the keys P_(k) and V_(k) and with the engines PGE and PVE. In alternative embodiments, the key(s) V_(k) may be provided to one or more distinguished nodes, called a validator node(s) in some literature. Note that the running of the engine KGE is a one-time operation whereas PGE may be run whenever additional proofs are needed.

Additionally, the TEE of client devices is pre-provisioned with illustrative computer programs Transfer, Split/Transfer, GCT and Merge.

FIG. 10B shows the general system for running one of the above illustrative programs. FIG. 10C describes the method used to run one of the illustrative programs.

In FIG. 10C, one of the programs Transfer, Merge, or Split/Transfer is selected and provided to PGE as input. PGE is also provided the input token(s) that may be needed by the selected program. The PGE runs the selected program. The selected program produces output tokens and data (if any). PGE also generates a proof data object using the trace produced by the instrumentation of the PGE. Finally, the method updates the ledger or record-keeper asynchronously.

Overview of Methods Effectuating Transactions

To illustrate the transfer of spending rights from one device to another, we present the following four illustrative programs. These programs have several features. One such feature, for example, is a solution to the double-spend problem. Other programs may also be defined that use various other features of the present invention.

-   -   1. Program “Transfer” takes inputs (Amount, From_(Device),         To_(Device), Token) and produces as output a data object         referred to as an “(output) token”. As will be seen from the         specification of the program, an execution of the program causes         a token with “Amount” to be transferred between the indicated         devices, i.e., the “from” and “to” devices. Note that the         program depletes the “Amount” completely, i.e., a zero balance         remains in the “From_Device” at the end of the transaction. The         output “token” details, inter alia, the transferred amount. As         will be further seen from the specification of the program, the         program becomes incapable of repeating the same execution a         second time. Correspondingly, a proof of an execution of the         program verifies the statement “amount reflected by token was         transferred between the indicated devices and the program cannot         repeat the execution”.     -   2. Program “Split/Transfer” takes inputs (Xfer_Balance,         From_Device, To_Device1, To_Device2, token) and produces as         output two data objects referred to as “token1” and “token2”.         The first token corresponds to the amount to be transferred to         the “To_Device1” from the “From_Device”. The second token         corresponds to the amount that is to be transferred from the         “From_Device” to itself, i.e., it is the balance that remains in         the “From_Device” after the transfer to the “To_Device”. As will         be further seen from the specification of the program, the         program becomes incapable of repeating the same execution a         second time. A successful execution of the program corresponds         to the statement that the program ran successfully and         transferred the first token from the “From_Device” to the         To_Device1” and the second token from the “From_Device” to         itself.     -   3. Program “Merge” takes as input two token data objects and         creates a single token as output. As will be seen from the         specification of the program, an execution of the program causes         a new token to be generated that represents the sum of the two         input tokens. As will be further seen from the specification of         the program, the program becomes incapable of repeating the same         execution a second time. Correspondingly, a proof of an         execution of the program verifies the statement “amount         reflected by output token represents the sum of the two input         tokens and the program cannot repeat the execution”.     -   4. Program “GCT” takes as input a request for a commitment         trigger, generates a random integer of a pre-determined size,         saves the generated integer in the TEE' s store, and provides         the same to the requesting program. It also receives and         verifies tokens and proofs.

A distinguishing feature of the above four programs (as will be explained below) is that after a first successful execution, they become incapable of a second successful execution on the same input token(s).

A malicious entity may gain access to these programs and modify them to produce a successful execution on the same input tokens by solving the discrete log problem. This is known to be extremely unlikely in the sense that it may require enormous time and computational effort due to the complexity of the discrete log problem that needs to be solved. Furthermore, the TEE will need to be compromised also since the programs reside and execute in the TEE.

A device upon receiving a proof, say P1 and token T1, may verify the proof as follows. The engine PVE (803) takes as input the proof object, P1, produced by PGE above, the key V_(k) produced by KGE above, and the output token(s) produced by the computer program inputted to PGE above. It produces a “yes” response if the proof P1 is linked to the indicated output token via the keys V_(k) and P_(k) (since the latter two keys are complementary). Otherwise, it produces the response “no”.

Decentralized Transactions with Asynchronous State Maintenance

In embodiments, a smart contract, i.e., a computer program, runs on one or more computers (M 1101, cf. FIG. 11) connected to a blockchain system/distributed database/record-keeper 1102. M 801 is shown as a single logical device in FIG. 11. In practice, it may be implemented as software running on a collection of servers. M 1101 is pre-provisioned with engines KGE and PGE (801 and 802, cf. FIG. 8A) and the programs Transfer, Split/Transfer, GCT and Merge. The engines KGE and PGE may be launched by user command or by an application program. These programs may then be provided any one of the programs Transfer, Split/Transfer, GCT and Merge as input.

In the descriptions to follow, we first describe a provisioning phase by which devices in the network are readied for transactions. We then describe the transactions themselves.

Provisioning Keys:

M 1101 launches the engine KGE (801, cf. FIG. 8A) to generate the keys P_(k) and V_(k) for each of the above four programs individually and distributes them to all client devices in the network such as 1103, 1104 and 1105. As noted above, this is a one-time process. In embodiments, the V_(k) may be provisioned to especially configured nodes of the network called validator nodes that may be used by client devices to verify transactions.

Provisioning “M” with Initial Spending Right:

M 1101 will be provisioned with an initial spending right using a pre-determined amount, say “Amt”. First, we provision M1101 with an initial commitment trigger, r1_(MM).

Notation: Recall that the subscripts, e.g., xy, of the commitment trigger “r_(xy)” denote that the trigger was generated and sent by device “x” to device “y”. In the case above, the term r1_(MM) denotes that the trigger generating and sending device is the same device, M.

Next, we request M 1101 to generate a second commitment trigger, i.e., r2_(MM).

We calculate C1=F(r1_(MM), m_(M)) and C2=F(r2_(MM), m_(M)), where m_(M) is the integer address of device M 1101. We now create the data structure “initial-token (Amt, C1, C2, C1*C2)”, where “Amt” is the pre-determined amount of the initial spending right. Finally, M 1101 deletes its initial commitment trigger, r1_(MM).

Thus, device M 1101 now possesses the spending right represented by the “initial token” and a saved commitment trigger r2_(MM).

Provisioning Client Devices with Programs:

In embodiments, users of the network are provisioned with trusted devices. Examples of such devices, without limitation, are smartphones, laptops, personal computers, etc. Each device contains an app, called a “wallet app”, meant to provide transaction services to users. For example, the wallet apps may display the user's token balance, past transaction history, etc. The TEE contained in the trusted devices is pre-provisioned with the computer programs, Split/Transfer, GCT, Transfer and Merge (described in detail later) and the engines PGE and PVE (802, 803 cf. FIG. 8A). Recall, that in the first provisioning step above, the trusted devices are provided the keys P_(K) and V_(K).

Three trusted client devices are shown as A, B and C in FIG. 11; these contain wallet apps, wallet₈₀₃, wallet₈₀₄ and wallet₈₀₅, respectively. Note that initially these wallets will show a zero balance and that the devices have no spending rights (tokens). The devices also do not possess saved commitment triggers since they have not engaged in any transactions yet. We assume that the devices “A”, “B” and “C” are synced, i.e., they have updated the record-keeper with all their previous transaction data.

M 1101 uses the method shown in FIG. 10C to transfer its spending right to device “A”, i.e., M 1101 needs to send an appropriately created token to “A”. Recall that as a result of the above provisioning process, “M” has acquired the spending right.

“M” requests “A” to provide it a new commitment trigger, r_(AM). Device “A” runs the following method (cf. FIG. 10D).

Method:

-   -   Launch engine PGE with program GCT as input.     -   PGE runs program GCT.     -   Program GCT receives request from device initiating device         (“M”), produces commitment trigger r_(AM), and saves it in the         TEE of recipient device (“A”).     -   GCT receives token and proof from initiating device (“M”) and         verifies them.     -   GCT produces a proof object, P, as output.     -   Program GCT terminates.     -   Program PGE produces “Proof” object as output.     -   Ledger/record-keeper is updated asynchronously with proof         object, P, (produced as output by GCT).

By running the above method, device “A” provides a commitment trigger, r_(AM), to device “M”. Thus, device “M” now possesses two commitment triggers, r2_(MM) (as a result of the provisioning step above) and r_(AM).

Device “M” now initiates the method shown in FIG. 10C that launches the program “Transfer” as input to PGE with input token, say T. PGE runs the program “Transfer” (described below). The program “Transfer” creates the token, token, comprising (Balance, C_(MM), C_(AM), C_(MM,AM)) where C_(MM)=F(r_(MM),m_(M)), C_(AM)=F(r_(AM), m_(A)), C_(MM,AM)=(C_(MM)*C_(AM)). Recall that m_(M) and m_(A) denote addresses of devices “M” and “A”, respectively.

In more detail, the “Transfer” program (FIG. 12) reads the saved commitment trigger, r1_(MM), from its store. If the trigger is not available, the program “Transfer” exits in failure.

Next, the program “Transfer” performs a series of calculations bracketed as “commitment calculation”. In the first step of the commitment calculation, we obtain the new commitment trigger, r_(AM), from device “A”. In the second step, we use the commitment trigger, r2_(MM), and the address of device “M” to calculate the commitment function “C_(MM)=F(r_(MM), m_(M))” (the function “F” is defined in 701, FIG. 7A). In the third step, we use the commitment trigger r2_(AM) and the address of device “A” to calculate the commitment function “C_(AM)=F(r_(AM), m_(AM))”. Finally, in the fourth step, we calculate C_(MM)*C_(AM).

The program is now ready to create the needed token with components (Bal, C_(MM), C_(AM), C_(MM,AM)).

The program “Transfer” now performs a sequence of steps as an “atomic” operation, i.e., the indicated steps are all performed without “interrupts” or none are performed. The sequence of steps is

-   -   Verify Balance is equal to the Amount designated as spending         right     -   Create the token     -   Destroy the commitment trigger, r2_(MM).

The token and proof are now available and may be sent to device “A”. The outputted proof object and token object represent a verification that the program “Transfer” ran and produced the output token, i.e., that the transfer from Device “M” to Device “A” was successfully performed. (We show later that the action also cannot be repeated.)

The method of FIG. 10C updates the ledger/record-keeper 1102 (FIG. 11) asynchronously and terminates execution.

Any entity, say device 1103, can use the engine PVE and key V_(k) (received in the provisioning steps above) to verify the received outputted token and proof object by using the PVE engine, i.e., the proof object, the received token and the key V_(k) are input to PVE to get the response “yes”. (In practice, the engines KGE, PGE and PVE and the keys V_(k) may be provisioned under network administrator control, i.e., received from one or more administrative nodes.)

Similarly, if M 1101 does not wish to transfer its entire balance to device “A”, it may use the program “Split/Transfer” to transfer a part of its balance. The working of the program “Split/Transfer” is described in detail below.

The two devices, “A” 1103 and “B” 1104, are now ready to initiate transactions since each device has tokens, i.e., spending rights. Note that device “C” 1105 does not have any spending rights and hence can only engage in receiving a transaction.

Note that the method of FIG. 10C may be used as a general method for inputting any of the four programs Transfer, Split/Transfer, Merge and GCT, to the engine PGE. The latter may then run the input program, take its output and generate a proof object that the indicated program was executed and produced the indicated output.

If now device “A” wishes to transact with device “B”, we may proceed as follows. (A fuller description follows later.)

Device “A” launches program wallet_(B) that, in turn, launches the method of FIG. 10C with program “Split/Transfer” as input to engine PGE. The program Split/Transfer outputs two tokens. The PGE outputs a proof object representing the proof that the indicated program (Split/Transfer) ran and produced two tokens.

Device “B” now has two tokens, one token that it received from device “M” (as a consequence of receiving a transaction from device “M”) and the second that it received from device “A”. It may consolidate the two tokens into a single token and update its state by executing a “Merge” transaction with itself.

We now describe the programs “Transfer”, “Split/Transfer” and “Merge” in more detail.

The Program, “Transfer”

Recall that as a result of the provisioning steps above, devices A, B and C contain the programs Transfer, Merge, Split/Transfer, and GCT in their respective TEE. They also contain wallet apps, wallet_(A), wallet_(B) and wallet_(C) (cf. FIG. 11).

We have described above the running of program “Transfer” by the method of FIG. 10C above. We now present the details of program “Transfer” with reference to FIG. 13. An exemplary purpose of the program is for device “M” to give spending rights to device “A”.

Device “M” launches its wallet app that, in turn, runs the program “Transfer” which starts by reading its commitment trigger, r2_(MM). (Recall that device “M” generated a commitment trigger for itself as described above.) If the latter is unavailable, the program exits in failure, implying the intended transaction cannot be executed.

Next, program “Transfer” performs the steps of the “commitment calculation” (as described above). Recall that this necessitates requesting a new commitment trigger, r_(AM), from device “A”. The program GCT is launched by device “A” when contacted by device “M”. FIG. 14 shows the flow chart for the program GCT. If the program GCT runs successfully, it returns the requested new commitment trigger, r_(AM).

Next the program “Transfer” enters an atomic phase (denoted by the square brackets). In an atomic phase, all instructions enclosed in square brackets (e.g., FIG. 12) are executed without interrupts and, furthermore, either all instructions in the block are executed or none are executed. The block in the Transfer program contains three instructions:

-   -   1. Verify that the amount of the spending right is equivalent to         the balance, Bal, of the token in the store.     -   2. If that is the case, create a token.     -   3. Destroy the saved commitment trigger, r2_(MM) (e.g., by         clearing a portion of the memory of the TEE).

Note, the program either terminates successfully by creating the token or exits in failure. In the former case, the newly created token (and proof) is sent to program GCT that verifies the received token (and proof).

The above transaction may be described using our succinct representation (introduced above) as follows.

<Device M[PGE/Transfer]{P1}{T1}{Bal}:P2[PGE/GCT]Device A>

where P1 denotes the proof that the program “Transfer” ran successfully in PGE and P2 denotes the proof that the program “GCT” running in PGE supplied the new commitment trigger and verified the received token. T1 denotes the token generated by the program “Transfer”. “Bal” is produced as output data by program “Transfer”.

Thus, the descriptions above illustrate the transference of spending rights from device “M” to device “A” using the program “Transfer”. Similarly, device “M” may transfer spending rights to device “B”, etc.

Program Split/Transfer

The operation of the Split/Transfer program may be described using our succinct notation (introduced above) as follows. Let us consider that device “A” wishes to initiate a transaction with device “B” using the program “Split/Transfer”. Specifically, we consider the exemplary case (FIG. 16) wherein device “A” with balance 100G (“G” being a unit of currency) intends to transfer 5G to device “B” whose balance is, say 50G. Thus, the former's balance needs to be decreased by 5G and the latter's balance needs to be increased by 5G as a result of the transaction. By way of example, the 100G spending right of device “A” may be the result of receiving the indicated spending right from device “M” in a previous transaction. Note that, since device “A” has a spending right, it must have a saved commitment trigger from a previous transaction.

The intended transaction is modeled as a pair of transactions, split/transfer (cf. FIG. 16). In the split/transfer transaction, we split device A's balance into two parts, 95G and 5G. Next, 5G is transferred to device “B” and 95G is transferred by device “A” to itself.

That is, we wish to undertake the following transactions (using the notational representation introduced above wherein “&&” denotes atomic execution of the two transactions); also shown in FIG. 15.

<Device A[PGE/SplitTransfer]{Proof}{Token}{5G}:{Proof}[PGE/GCT]Device B>

&&

<Device A[PGE/SplitTransfer]{Proof}{Token}{95G}:{Proof}[PGE/GCT]>

Note that we need not specify the “receiving” device in our notation when the initiating and receiving devices are the same.

In the program Split/Transfer, we calculate C_(MA), C_(AA) and C_(MA)*C_(AA) as shown in (1720) FIG. 17. The token that is computed is shown in 1720, FIG. 17 with balance 95G. Next, we compute C_(BA) and C_(MA)*C_(BA). The token that is computed is shown in (1710, cf. FIG. 17) with balance 5G.

FIG. 18 shows the Split/Transfer program and FIG. 19 shows a flow chart of the same. Both figures show the computing of the two needed commitment functions and creating the two needed tokens by device “A”. One token is for transferring spending rights from device “A” to device “B” and the second to itself. Note that in the case of the “Split/Transfer” program, two commitment triggers are generated (one for each token).

The Program “Merge”

The “Merge” program is shown in FIGS. 21, 22 and 23. Its succinct representation is shown in FIG. 20. In this case, we assume device B has two tokens with balances “bal_1” and “bal_2”. Therefore, it must have two saved commitment triggers from previous transactions. Let device “B” have previous interactions with devices “1” and “2”. Thus, it has commitment triggers, r_(B1) and r_(B2), respectively, saved as a result of those previous transactions.

Device “B” uses program “Merge” to do a transaction with itself, hence it generates a commitment trigger r_(BB) for itself.

Program “Merge” creates a new token whose balance is the aggregate (bal_1+bal_2). Note that in this case, the commitment function uses three parameters. Using the succinct representation introduced above, we may describe the merge transaction as follows.

<Device B[PGE/Merge]{Proof}{Token}{5G}{50G}:{Proof}[PGE/GCT]>

Optimization

In embodiments, the size of the data messages between two interacting devices, i.e., nodes of the network, may become large since the messages contain proof objects. To reduce the size of the messaging traffic and traffic load on the network, a policy may be instituted that requires client devices to periodically update the record-keeper. One such policy has been described earlier in the context of “synced” devices.

That is, a client device may provide the list of proofs and tokens for all its transactions along with its address serving as a unique identifier, to the record-keeper. In one embodiment, the record-keeper may generate a Merkle node from the provided data (proofs, tokens and addresses) as a special marker to the client device. An initiating device may now present the marker in lieu of its list of proofs while executing a transaction. Upon receipt of a marker, the receiving device may provide the address of the client that sent the marker along with the marker to the record-keeper who may verify the provided data elements using the well-known mechanism of Merkle trees.

Note on Asynchronous Updates

We have previously described the use of commitment triggers and that, if a trigger is unavailable, the ensuing computer program to compute it may require enormous time and resources. Now, as described above, after a transaction is executed, the initiating device executes an asynchronous update of the record-keeper or ledger. We propose that the asynchronous updating method be designed to effectuate the update within a pre-determined time after the conclusion of the transaction. Thus, a malicious attempt to compute the commitment trigger will be time-constrained.

Lost Devices or Loss of Network Connectivity

The following possibility with respect to FIG. 10C and elsewhere should be noted. It is possible that after step 5 has been executed and before step 6 has been initiated or finished, one or both of the devices engaged in the transaction may be lost or malfunction or lose network connectivity, etc. Thus, the transaction would be completed as far as the devices are concerned but the log may not be updated. We resolve this situation as follows.

In embodiments, we require that if two devices, say “A” and “B” are engaged in a transaction, we locate one or more devices, called proxy devices. The number of proxy devices so located may be pre-determined or the number may be a function of the amount of the transaction being executed between devices “A” and “B”. The number of proxy devices may also be determined by a system or user stated policy.

Once the required number of proxy devices have been located, “A” and “B” may executed the transaction and provide an update to the one or more proxy devices in an atomic operation. That is, with respect to FIG. 12 (by way of example), the atomic operation in step 7:

7. [Verify Bal==Amount && Create and output token=(Bal, C_(MM), “blank”, C_(MM,AM),) && Destroy r1_(MM)]

is replaced by a new step 7 and an additional step number 8 is added as follows.

new step 7. Locate proxy devices. If required number not found, exit.

Additional step 8. [Verify Bal==Amount && Create and output token=(Bal, C_(MM), “blank”, C_(MM,AM),) && Destroy r1_(MM) && update proxy devices]

Thus, in case device “A” and “B” are lost or malfunction, the proxy devices may be requested to update the log. For example, having received an update, a proxy device may periodically check the log and ascertain that a corresponding update has been done. If, after a pre-determined amount of time, no such update is detected, the proxy device may effectuate the updating of the log.

The systems and methods described herein may be used in a wide variety of applications other than the currency applications described in detail above. For instance, in addition to a currency value or a spending value, the systems and techniques described herein may be used in transactions involving, without limitation, credentials, property rights, status information, real estate, insurance, health care, music and other royalties, and so on. That is, more generally, the systems and techniques described herein may be used to transfer the value of any state between client devices. Such states may specify or otherwise involve, without limitation, financial data, public and private records, identification, attestation, loyalty points, electronic coupons, smart contracts, escrow records, and so on.

Towards this goal, we consider a fault-tolerance application in which various components of the network report their status to a log or record-keeper. One or more entities may then peruse the log to discern the status of the components. It is required that no inconsistent status information be communicated to the log.

To use the methods of the current invention in this application, we may modify the “Transfer” program as follows.

We use the data field of the token data structure computed by the “Transfer” program to encode the status of a device. For example, the status information may indicate that the device is functioning normally or malfunctioning. A device with such a suitably modified program may then be programmed to execute a transaction resulting in the transaction data being logged in the record-keeper.

To execute a transaction, a device needs to be provisioned with a spending right and the suitably modified “Transfer” program. To this purpose, we may use the M-device 1101 of FIG. 11 to provision network devices with spending rights and the modified “Transfer” program. (In the context of the current fault-tolerance embodiment, it may be more appropriate to refer to the spending right as a “communication right”.)

Having been provisioned with a communication right and the suitably modified Transfer program, a device may use the latter to execute a transaction with itself. Such a transaction will cause the transaction data to be recorded in the log. If the device is programmed to periodically undertake such transactions, the corresponding log entries will then contain the history of the device's status. As a consequence of a transaction, the device's spending/communication right is effectively renewed.

Further note that if a malicious entity modifies a device's “Transfer” program, the ensuing transaction undertaken by the device will not be verified as per the program proof process described earlier.

Thus, a consistent view of the current and historical status of the network's devices may be obtained from the log's records.

As used herein the terms “software,” computer programs,” “programs,” “computer code” and the like refer to a set of program instructions running on an arithmetical processing device such as a microprocessor or DSP chip, or as a set of logic operations implemented in circuitry such as a field-programmable gate array (FPGA) or in a semicustom or custom VLSI integrated circuit. That is, all such references to “software,” computer programs,” “programs,” “computer code,” as well as references to various “engines” and the like may be implemented in any form of logic embodied in hardware, a combination of hardware and software, software, or software in execution. Furthermore, logic embodied, for instance, exclusively in hardware may also be arranged in some embodiments to function as its own trusted execution environment.

Illustrative Computing Environment

As discussed above, aspects of the subject matter described herein may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and so forth, which perform particular tasks or implement particular abstract data types. Aspects of the subject matter described herein may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.

Also, it is noted that some embodiments have been described as a process which is depicted as a flow diagram or block diagram. Although each may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be rearranged. A process may have additional steps not included in the figure.

The claimed subject matter may be implemented as a method, apparatus, or article of manufacture using standard programming and/or engineering techniques to produce software, firmware, hardware, or any combination thereof to control a computer to implement the disclosed subject matter. For instance, the claimed subject matter may be implemented as a computer-readable storage medium embedded with a computer executable program, which encompasses a computer program accessible from any computer-readable storage device or storage media. For example, computer readable storage media can include but are not limited to magnetic storage devices (e.g., hard disk, floppy disk, magnetic strips . . . ), optical disks (e.g., compact disk (CD), digital versatile disk (DVD) . . . ), smart cards, and flash memory devices (e.g., card, stick, key drive . . . ). However, computer readable storage media do not include transitory forms of storage such as propagating signals, for example. Of course, those skilled in the art will recognize many modifications may be made to this configuration without departing from the scope or spirit of the claimed subject matter.

Moreover, as used in this application, the terms “component,” “module,” “engine,” “system,” “apparatus,” “interface,” or the like are generally intended to refer to a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer. By way of illustration, both an application running on a controller and the controller can be a component. One or more components may reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers.

The foregoing described embodiments depict different components contained within, or connected with, different other components. It is to be understood that such depicted architectures are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermediary components. Likewise, any two components so associated can also be viewed as being “operably connected”, or “operably coupled”, to each other to achieve the desired functionality. 

1. A method of performing a transaction between a first communication device and a second communication device over a communication network, comprising: requesting, with the first communication device, at least a first integer value from the second communications device, the first integer value being generated for use only in the transaction between the first and second communication devices, said first and second communication devices being provisioned with (i) first and second complementary cryptographic keys that are provided by a trusted party, the first key being usable to generate a proof that verifies that computer logic used a given input to produce a given output and the second key being usable to verify that the proof is accurate; (ii) a proof generating engine (PGE) that uses the computer logic and the first key as inputs and provides as outputs a first proof and a token that is an output arising from execution of the CP; and (ii) a proof verification engine (PVE) that uses the proof, the second key and the token as inputs and output indicating if the proof is accurate; calculating, with the first communication device, a first value of an irreversible function that uses as an input the first integer value received from the second communication device; executing in an atomic operation, with the first communication device, the computer logic to generate the token and a first proof and permanently delete the first integer value, the first proof being usable to verify that the computer logic generated the token, the token including (i) a state value that is to be transferred from the first communication device to the second communication device, (ii) a second value of the irreversible function, the second value of the irreversible function being calculated by a third communication device that transferred the state value to the first communication device, wherein the input to the irreversible function when calculating the second value includes a second integer value received by the third communication device from the first communication device and (iii) a product of the first value of the irreversible function and the second value of the irreversible function; and sending, in one or more data messages, the token and the first proof to the second communication device from the first communication device.
 2. The method of claim 1, wherein calculating the first value of the irreversible function uses as another input to the irreversible function an identifier of the second communication device.
 3. The method of claim 1, wherein calculating the second value of the irreversible function uses as another input to the irreversible function an identifier of the first communication device.
 4. The method of claim 1, wherein the state value is a currency value to be transferred from the first communication device to the second communication device.
 5. The method of claim 1, wherein the first integer value is a randomly generated value generated by the second communication device.
 6. The method of claim 1, wherein the one or more data messages sent by the first communication device to the second communication device further includes a first hash value that is a hash of a combination of a second token generated by the third communication device and sent to the first communication device and a second proof that verifies that the third communication device generated the second token.
 7. The method of claim 6, wherein the one or more data messages sent by the first communication device to the second communication device further includes a second hash value that is a hash of a combination of the token generated by the first communication device and sent to the second communication device, the first proof and the first hash value.
 8. The method of claim 1, wherein the calculating and executing are performed in a trusted execution environment of the first communication device.
 9. A method of performing a transaction between a first communication device and a second communication device over a communication network, comprising: generating, with the second communication device, at least a first integer value, the first integer value being generated for use only in the transaction between the first and second communication devices, said first and second communication devices being provisioned with (i) first and second complementary cryptographic keys that are provided by a trusted party, the first key being usable to generate a proof that verifies that computer logic used a given input to produce a given output token and the second key being usable to verify that the proof is accurate; (ii) a proof generating engine (PGE) that uses the computer logic and the first key as inputs and provides as outputs a proof and the given output token; and (ii) a proof verification engine (PVE) that uses the proof, the second key and the token as inputs and output indicating if the proof is accurate; sending the first integer value from the second communication device to the first communication device; receiving at the second communication device, in one or more data messages from the first communication device, the given output token and the proof; using the first proof, the second key and the token as inputs to the PVE to verify that the computer logic generated the given output token, the token including (i) a state value that is to be transferred from the first communication device to the second communication device, (ii) a first value of an irreversible function, the first value of the irreversible function being calculated by a third communication device that transferred the state value to the first communication device, wherein the input to the irreversible function when calculating the first value includes a second integer value received by the third communication device from the first communication device and (iii) a product of the first value of the irreversible function and a second value of the irreversible function that is calculated by the first communication device using the first integer value as an input value.
 10. A method for transferring a state value from a first communication device directly to a second communication device, comprising: requesting a data element from the second communication device; calculating a value of an irreversible function using the data element as an input to the irreversible function; encapsulating the state value in a data object using the calculated value of the irreversible function; transferring the data object from the first communication device to the second communication device; and wherein the first communication device can repeat the transferring of the state value only by solving the irreversible function in a reverse direction.
 11. The method of claim 10, further comprising generating the data object using computer logic and generating a proof representing that the computer logic generated the data object.
 12. The method of claim 11, wherein transferring the data object further includes transferring the proof to the second communication device.
 13. The method of claim 12, wherein the second communication device is pre-provisioned with a first cryptographic key usable to verify that the proof is accurate.
 14. The method of claim 13, wherein the first communication device is pre-provisioned with a second cryptographic key complementary to the first cryptographic key and being usable to generate the proof.
 15. The method of claim 11, wherein the calculating, generating and encapsulating is performed in a trusted execution environment of the first communication device.
 16. The method of claim 11, further comprising permanently deleting the data element from the first communication device in an atomic operation with generating the data object. 